NUT-12: Chaum-Pedersen DLEQ proofs

[callebtc]

Chaum-Pedersen DLEQ proofs

In this document, we present an extension of Cashu's crypto system to allow a user Alice to verify the mint Bob's signature using only Bob's public keys. We explain how another user Carol who receives ecash from Alice can execute the DLEQ proof as well. This is achieved using a Discrete Log Equality (DLEQ) proof. Previously, Bob's signature could only be checked by himself using his own private keys (NUT-00).

More resources:

• Implementation in Nutshell: https://github.com/cashubtc/cashu/pull/175
• A discussion about the DLEQ proof on Somsens's gist
• A discussion on the pros and cons compared to an alternative approach: https://github.com/cashubtc/nutshell/pull/295

Todo:

• [x] Describe DLEQ proof
• [x] Alice validates Bob's DLEQ proof
• [x] Carol validates Alice's DLEQ proof